Can not sign in to Adobe Acrobat Reader in my mobile (android)

Try this:

• Turn on  your mobile device's  Airplane Mode, then turn off Airplane Mode, verify that your connection and data is up,  and try to sugn in again.
• If that doesn't work, then try by clearing the mobile app's cache, and also put to sleep other applications that may be running in the background.

Depending on what AndroidOS version you have you can clear the temporary memory and background processes by using the "Device maintenance" app.

• If none of these tips work, I would try to uninstall and reinstall the app.

However, I would say that if I was having this problem in my device, to go online and  check if you can Sign In to your account online via web browser.

There were a few connectivity issues yesterday, even to log in to the support forums. 

It is possible that there  was an unnanounced server maintenance going on when you attempted to sig in with your app.